Comment by codebje

Well of course hardware fails, and of course verification doesn't make things work perfectly. Verification says the given design meets the specification, assumptions and all. When the assumptions don't hold, the design shouldn't be expected to work correctly, either. When the assumptions do hold, formal verification says the design will work correctly (plus or minus errors in tools and materials).

We know dynamic RAM is susceptible to bit-flip errors. We can quantify the likelihood of it pretty well under various conditions. We can design a specification to detect and correct single bit errors. We can design hardware to meet that specification. We can formally verify it. That's how we get ECC RAM.

CPUs are almost never formally verified, at least not in full. Reliability engineering around systems too complex to verify, too expensive to engineer to never fail, or that might operate outside of the safe assumptions of their verified specifications, usually means something like redundancy and majority-rules designs. That doesn't mean verification plays no part. How do you know your majority-rules design works in the face of hardware errors? Specify it, verify it.